Working Paper: NBER ID: w23232
Authors: Zhuan Pei; Jrn-Steffen Pischke; Hannes Schwandt
Abstract: Researchers frequently test identifying assumptions in regression based research designs (which include instrumental variables or difference-in-differences models) by adding additional control variables on the right hand side of the regression. If such additions do not affect the coefficient of interest (much) a study is presumed to be reliable. We caution that such invariance may result from the fact that the observed variables used in such robustness checks are often poor measures of the potential underlying confounders. In this case, a more powerful test of the identifying assumption is to put the variable on the left hand side of the candidate regression. We provide derivations for the estimators and test statistics involved, as well as power calculations, which can help applied researchers interpret their findings. We illustrate these results in the context of various strategies which have been suggested to identify the returns to schooling.
Keywords: Causal inference; Measurement error; Regression analysis
JEL Codes: C31; C52
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| years of schooling (I21) | log wages (J31) |
| poorly measured confounder on the right side of the regression (C20) | omitted variable bias (C20) |
| confounder on the left side of the regression (C29) | balancing test effectiveness (C90) |
| measurement error in confounders (C83) | omitted variables bias (C20) |
| balancing test (J78) | power of regression strategies (C29) |